Greatest Common Factor (GCF) Calculator

Enter numbers separated by commas , or spaces (Maximum 20 numbers) and click "Calculate". Example values are preloaded to help you understand.

Calculation Results

What is the Greatest Common Factor?

The Greatest Common Factor (GCF) is the largest number that divides two or more numbers exactly. Another name is Greatest Common Divisor (GCD). It helps simplify fractions and solve math problems.

Examples:

  • The GCF of 12 and 18 is 6.
  • The GCF of 6 and 9 is 3.
  • The GCF of 24 and 36 is 12.

How to Find the Greatest Common Factor

There are several ways to find the GCF. The most common methods are:

  1. Prime Factorization
  2. Division Method
  3. Listing Factors

1. Using Prime Factorization

Prime factorization breaks numbers into prime numbers multiplied together. Then, we multiply the common prime factors to find the GCF.

Example 1:

Find the GCF of 24 and 36.

Number Prime Factorization
24 2 × 2 × 2 × 3
36 2 × 2 × 3 × 3

Common prime factors: 2 × 2 × 3

GCF = 2 × 2 × 3 = 12

Example 2:

Find the GCF of 18 and 12.

Number Prime Factorization
18 2 × 3 × 3
12 2 × 2 × 3

Common prime factors: 2 × 3

GCF = 2 × 3 = 6

2. Using the Division Method

We divide the larger number by the smaller number. Then, we divide the divisor by the remainder until the remainder is 0. The last divisor is the GCF.

Example:

Find the GCF of 48 and 18.

  1. 48 ÷ 18 = 2 remainder 12
  2. 18 ÷ 12 = 1 remainder 6
  3. 12 ÷ 6 = 2 remainder 0

GCF = 6

3. Listing Factors Method

List all factors of the numbers. The largest factor that is common to both numbers is the GCF.

Example:

Find the GCF of 20 and 12.

Number Factors
20 1, 2, 4, 5, 10, 20
12 1, 2, 3, 4, 6, 12

Common factors: 1, 2, 4

GCF = 4

Formula to Calculate GCF using Prime Factorization

If numbers are A and B:

1. Break A and B into prime factors.
2. Multiply all common prime factors.
3. Result is GCF(A, B)

Example: GCF(24, 36) = 2 × 2 × 3 = 12

Step-by-Step Solution Using Calculator

  1. Enter numbers separated by commas or spaces.
  2. Click "Calculate".
  3. The calculator shows prime factorization of each number.
  4. Common factors are multiplied automatically.
  5. The final GCF is displayed.

Examples Using Calculator

Numbers GCF
12, 18 6
6, 9 3
24, 36 12
20, 12 4
6, 8 2

Benefits of Using This Calculator

  • Saves time compared to manual calculation.
  • Shows step-by-step prime factorization.
  • Helps students understand GCF clearly.
  • Can handle up to 20 numbers at once.
  • Includes reset and copy result features.

Frequently Asked Questions (FAQs)

Q1: What is the greatest common factor?

A: It is the largest number that divides two or more numbers exactly.

Q2: How do I find the greatest common factor?

A: Use prime factorization, division method, or list all factors and pick the largest common one.

Q3: What is the GCF of 12 and 18?

A: GCF(12, 18) = 6

Q4: What is the greatest common factor of 6 and 9?

A: GCF(6, 9) = 3

Q5: What is the greatest common factor of 24 and 36?

A: GCF(24, 36) = 12

Q6: How do I use the calculator?

A: Enter numbers, click Calculate, see results with steps. Reset if needed.

Q7: Can I enter more than two numbers?

A: Yes, up to 20 numbers separated by commas or spaces.

Q8: What is the GCF of 6 and 8?

A: GCF(6, 8) = 2

Q9: Why is GCF important?

A: GCF is used to simplify fractions and solve number problems.

Q10: Can the calculator show prime factorization?

A: Yes, it shows prime factorization for all numbers entered.

Q11: What is the GCF of 8 and 12?

A: GCF(8, 12) = 4

Q12: What is the GCF of 20 and 12?

A: GCF(20, 12) = 4

Q13: Can I copy the result?

A: Yes, click the Copy Result button at the bottom of the result box.

Q14: What if I enter invalid numbers?

A: The calculator will alert you to enter valid numbers.

Q15: What is the GCF of 18 and 12?

A: GCF(18, 12) = 6

Q16: Can the calculator help with worksheets?

A: Yes, it can provide answers for common GCF problems quickly.

Q17: How do I reset the calculator?

A: Click the Reset button. It restores example numbers and clears results.

Q18: Can I find GCF of more than two numbers?

A: Yes. Enter all numbers separated by commas or spaces.

Q19: What is the GCF of 9 and 6?

A: GCF(9, 6) = 3

Q20: What is the GCF of 6 and 12?

A: GCF(6, 12) = 6

Q21: What is the GCF of 12, 18, and 24?

A: GCF(12, 18, 24) = 6

Q22: Can the calculator handle zero?

A: No, do not enter zero. GCF is not defined for zero.

Q23: What is a greatest common factor?

A: Another term for GCF or greatest common divisor (GCD).

Q24: How is GCF used in fractions?

A: To simplify fractions, divide numerator and denominator by the GCF.

Q25: Is GCF same as LCM?

A: No, GCF is largest common factor, LCM is smallest common multiple.

Q26: Can I find GCF of negative numbers?

A: Yes, use absolute values of numbers.

Q27: What is the GCF of 15 and 25?

A: GCF(15, 25) = 5

Q28: What is the GCF of 40 and 60?

A: GCF(40, 60) = 20

Q29: Can I use this calculator for homework?

A: Yes, it can help solve GCF problems step by step.

Q30: How to use the prime factorization formula?

A: Break numbers into primes, list common factors, multiply them. That is the GCF.